@ARTICLE{10.21494/ISTE.OP.2020.0582, 

TITLE={Random walk on finite extensions of lattices}, 
  
AUTHOR={Vignon Oussa, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={12}, 

NUMBER={Issue 1 (January 2021)}, 
	
YEAR={2021}, 

URL={http://openscience.fr/Random-walk-on-finite-extensions-of-lattices}, 
	
DOI={10.21494/ISTE.OP.2020.0582}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={We obtain a precise formula for the probability that a random walker returns to the origin after n steps on some semi-direct product groups obtained by extending a Euclidean lattice by a finite group. Prior to this work, to the best of our knowledge, for the class of groups considered, only asymptotic estimates were available in the literature.}}